Method for fabricating Luneberg lens

ABSTRACT

A method for fabricating a Luneberg lens is disclosed. A plurality of cubes are secured together to form a sphere. The sphere is then cut into thin slices about one axis and the slices are reassembled out of registry in the angular coordinate. The sphere is then sliced along the second axis and these slices are again reassembled out of registry in the angular coordinate. Finally, the sphere is cut into small slices about the third axis and these slices are then again reassembled out of registry in the angular coordinate. This method of fabricating a Luneberg lens results in a reduction in the size of the inhomogeneities by a large degree; and therefore, results in a large improvement in the high frequency characteristics of the Luneberg lens.

United States Patent [191 Andrews METHOD FOR FABRICATING LUNEBERG LENS [76] Inventor: William J. Andrews, 9633 Parkwood Drive, Bethesda, Md.

[22] Filed: Jan. 14, 1974 [21] Appl. No.: 432,999

[ Oct. 21, 1975 Primary Examiner-Eli Lieberman Attorney, Agent, or FirmWitherspoon and Lane [57] ABSTRACT A method for fabricating a Luneberg lens is disclosed. A plurality of cubes are secured together to form a sphere. The sphere is then cut into thin slices about one axis and the slices are reassembled out of registry in the angular coordinate. The sphere is then sliced along the second axis and these slices are again reassembled out of registry in the angular coordinate. Finally, the sphere is cut into small slices about the third axis and these slices are then again reassembled out of registry in the angular coordinate. This method of fabricating a Luneberg lens results in a reduction in the size of the inhomogeneities by a large degree; and therefore, results in a large improvement in the high frequency characteristics of the Luneberg lens.

6 Claims, 4 Drawing Figures US. Patent Oct. 21, 1975 3,914,769

I I l FIG. I

FIG. 2

Y 3 FIG. 3

FIG. 4

METHOD FOR FABRICATING LUNEBERG LENS The invention described herein may be manufactured, used, and licensed by or for the Government for Governmental purposes without the payment to me of any royalties thereon.

BACKGROUND OF THE INVENTION This invention relates to Luneberg lenses, and more particularly to a method of making Luneberg lenses.

At present two methods are most often used to fabricate Luneberg lenses. The first method is to construct the lens in a layer of sheets and control the dielectric constant by drilling holes, milling slots, or otherwise removing material from the disc. The second method generally used is to construct the lens as a series of spherical shells of graded dielectric constant.

In the first method described above, the milling or drilling operation is very costly. Further, the sizes of the irregularities must be much less than one-fourth wavelength or one-fourth inch at 12 GHz. This calls for exceptionally precise and costly fabrication. Further, it is not at all clear just how fine the holes must be. In addition, with this method the index of the lens is usually calculated by the Clausius-Mossetti law which makes some assumptions about the homogeneity of the material. These assumptions may not prove accurate in a given case. 7

The second method described above is also not free of problems. With this method, a very large number of layers are required to provide a lens that works reliably at, for example, 12 GHz. It is difficult to make such large pieces of material of uniform density. The lack of uniform density will result in degradation of the high frequency characteristics of the lens.

The method of this invention overcomes most of the problems of the two methods described above, and at the same time provides a Luneberg lens having improved high frequency characteristics.

' SUMMARY OF THE INVENTION Luneberg lenses are fabricated in accordance with this invention by fabricating a sphere from a plurality of cubes. The cubes are cemented together to form the sphere. After the sphere is formed, it is sliced into thin.

slices along one of its axis. The slices are then reassembled out of registry in the angular coordinate. The sphere is then sliced in thin slices along its second axis and again reassembled out of registry in the angular coordinate. Finally, the sphere is cut in slices along its third axis and these slices are again reassembled out of registry in the angular coordinate. By this method, a large reduction in the size of the inhomogeneities is provided with a consequent large improvement in the high frequency characteristics of the Luneberg lens.

I BRIEF DESCRIPTION OF THE DRAWING A complete understanding of the invention can be obtained by a reading of the following detailed description' when read in conjunction with the annexed drawings in which:

FIG. 1 shows a cube used to fabricate the basic lens;

FIG. 2 shows a sphere fabricated from the cubes of FIG. 1; and

FIGS. 3 and 4 are diagrams useful in describing the invention.

DETAILED DESCRIPTION OF THE INVENTION Referring to FIG. 1, cubes such as the cube 1 are cut from batches of foam-like material. The cubes 1 can be tested and labeled with their indices of refraction, or the index of refraction can be determined by theoretical calculations using a digital computer.

The cubes 1 are then cemented together to form a sphere such as the sphere 3 shown in FIG. 2. Of course, the outer cubes would have to be ground down to form a smooth sphere such as the sphere shown in FIG. 2. While the correspondence of the index of refraction would, of course, not be exact by cementing the cubes together, it would provide a high degree of accuracy,

on an average.

Now that the sphere 3 has been formed, the next steps of the method of this invention are carried out. FIGS. 3 and 4 are given to describe the balance of the invention. These figures are to be considered as illustrations only. They do not represent precisely what takes place within the Luneberg lens. While FIGS. 3 and 4 show only one of the cubes used to make up sphere 3, the following description applies to all of the cubes 1 in the sphere 3. Referring to FIG. 3, the sphere 3 is shown with one of the cubes 1 illustrated therein. The numerals 6, 7, 8 and 9 represent slices that are to be taken through this cube 1 along, for example the Z axis. The entire sphere 3 is cut into such slices along the Z axis. The exact thickness of these slices is not critical. For example, the slices may range in thickness from one-eighth inch to one-fourth inch. The slices can be thinner or thicker. As will become apparent, as thin a slice as is practical is preferable. These slices are all rotated angularly relative to one another and the cube is again reassembled. FIG. 4 illustrates what happens as given slices are taken out of cube 1 and rotated relative to each other. After the sphere 3 is cut into thin slices along the axis, these slices are rotated angularly. Considering one of the cubes, cube 1 of FIG. 3 and the slices 6, 7, 8, and 9, it is obvious that these slices which are part of the sphere slice will no longer be one on top of the other as shown in FIG. 3. Instead, slices 6, 7, 8

and 9 will be displaced angularly relative to each other. FIG. 4 illustrates the relative displacement of slices 6, 7, 8 and 9 of cube 1 of FIG. 3. It is assumed that the slices of sphere 3 of which illustrated slices 6, 7, 8 and 9 are a part have been rotated such that slices 6, 7, 8 and 9 now occupy the positions shown in FIG. 4 within sphere'3. All the cubes 1 used to make up sphere 3 will also have equivalent slices displaced a selected amount relative to each other as the slices 6, 7, 8 and 9 are displaced relative to each other. A single cube and its slices are shown in FIGS. 3 and 4 rather than the entire sphere slices since it would be difficult to show the principle involved by showing a complete slice of the sphere. However, what takes place is that the entire sphere 3 of FIG. 2 is cut into these thin slices and then the slices are rotated relative to each other. Thus, every cube 1 of sphere 3 is sliced in the manner shown in FIGS. 3 and 4 and these slices of everycube wind up out of registry with one another in the angular coordinate. Of course, since the cubes are cemented together, the slices are flat circular discs. Therefore, any points adjacent to one another in each of the cubes 1 used to make up sphere 3 will now be displaced by the degree of relative angular rotations of the slices.

After the sphere 3 has been cut into the slices along the Z axis and these slices are rotated as described above, sphere 3 is reassembled by cementing these slices together to reform sphere 3. Sphere 3 is then cut into thin slices along its X axis and these slices are rotated angularly out of registry as described above with respect to the Z axis. After these X axis slices are rotated, the slices are again cemented to reform sphere 3. Sphere 3 is then cut into thin slices along the third or Y axis and these slices are rotated angularly out of registration. After these Y axis slices are rotated, they are cemented together to again form sphere 3.

Considering FIGS. 3 and 4 and the above description, it should be apparent that all the cubes 1 used to make up sphere 3 wind up into pieces that are distributed throughout sphere 3 in the manner illustrated with the single cube 1 shown in FIGS. 3 and 4. The distribution depends upon the number of slices taken and the rotation of slices.

This slicing and reassembling after rotation of the slices results in a large reduction in the inhomogeneities in the material. This results in a large improvement in the high frequency characteristics of the Luneberg lens. Further, when compared to the typical prior art methods used of forming Luneberg lenses, this method is considerably less expensive.

Since the primary purpose of slicing sphere 3 and rotating the slices is to reduce the inhomogeneities in the material, it is obvious that many thin slices are preferable over thick slices and that it is preferable to take slices along the three axes as described rather than along only one axis. However, as mentioned, there is no exact critical size for the slices. Even a relatively small number of thick slices will result in some improvement of the Luneberg lens formed by sphere 3. Further, taking slices along only one axis or along two axes instead of three will also result in an improvement over the lens formed by sphere 3. However, as a general rule sphere 3 will be cut into very thin slices along all three axes to fabricate the final Luneberg lens. This process of taking slices along all three axes and rotating the slices results in a large reduction in the inhomogeneities in the material with a resultant improvement in the high frequency characteristics of the lens. The degree of improvement in the high frequency characteristics will diminish as the slices become larger and will be smaller if slices are taken along one axis only.

A further refinement of the lens can be obtained, if necessary, by shifting the slices in translation as well as in angle. Shifting the slices in angle, as described above, does not effect the radial distribution, but shifting the slices in translation may have a small beneficial effect. However, the shift in translation is not necessary.

From the foregoing description, it should be apparent that this invention provides a relatively inexpensive method of fabricating a Luneberg lens, and further provides a Luneberg lens having a high degree of refinement since the method breaks up the lens elements into smaller scattering volumes. By reducing the size of the scattering volumes, the efficiency of the lens is greatly improved.

While the invention has been described with reference to a particular method, it will be apparent to those skilled in the art that various changes and modifications can be made to the invention without departing from the spirit and scope of the invention as set forth in the claims. For example, the basic sphere could actually be made by the layering of sheets and milling and drilling as described above. However, this would not be a preferable method of making the basic sphere since it would increase the cost of fabricating the Luneberg lens. It should be pointed out, however, that this method does not lend itself to a lens in which the basic sphere is made from a series of spherical shells, as described above.

What is claimed is:

1. A method for constructing a Luneberg lens comprising the following steps:

a. cutting a batch of Luneberg lens material into cubes;

b. determining the indices of refraction of said cubes;

c. cementing said cubes together in accordance with their respective indices of refraction to form a first approximation of a Luneberg lens sphere;

d. cutting said sphere into thin slices along a first axis;

and

e. reassembling said slices out of registry in an angular coordinate to again form said sphere.

2. The method as described in claim 1 wherein said sphere formed by said reassembled slices is again cut into thin slices along a second axis and wherein said slices cut from said reassembled sphere are reassembled out of registry in an angular coordinate to again form said sphere.

3. The method as described in claim 2 wherein said sphere formed by reassembling said slices cut from along said second axis is again cut into thin slices along its third axis and said thin slices out along said third axis are reassembled out of registry in an angular coordinate to again form said sphere.

4. The method as described in claim 3 wherein said cubes are cut from batches of foam-like material.

5. The method as described in claim 3 wherein said slices cut along said first axis, said slices cut along said second axis, and said slices cut along said third axis are all of approximately equal thickness.

6. The method as described in claim 5 wherein said thickness of all said slices lies within the range of onefourth inch to one-eighth inch. 

1. A method for constructing a Luneberg lens comprising the following steps: a. cutting a batch of LunEberg lens material into cubes; b. determining the indices of refraction of said cubes; c. cementing said cubes together in accordance with their respective indices of refraction to form a first approximation of a Luneberg lens sphere; d. cutting said sphere into thin slices along a first axis; and e. reassembling said slices out of registry in an angular coordinate to again form said sphere.
 2. The method as described in claim 1 wherein said sphere formed by said reassembled slices is again cut into thin slices along a second axis and wherein said slices cut from said reassembled sphere are reassembled out of registry in an angular coordinate to again form said sphere.
 3. The method as described in claim 2 wherein said sphere formed by reassembling said slices cut from along said second axis is again cut into thin slices along its third axis and said thin slices cut along said third axis are reassembled out of registry in an angular coordinate to again form said sphere.
 4. The method as described in claim 3 wherein said cubes are cut from batches of foam-like material.
 5. The method as described in claim 3 wherein said slices cut along said first axis, said slices cut along said second axis, and said slices cut along said third axis are all of approximately equal thickness.
 6. The method as described in claim 5 wherein said thickness of all said slices lies within the range of one-fourth inch to one-eighth inch. 